Optimizing Portfolios of Cointelated Pairs with Stochastic Control and Machine Learning

Summary

This work compares financial mathematics and machine learning for dynamic portfolio optimization of two intertwined assets over a continuous-time, finite horizon. Its financial mathematics approach uses a cointelation model intended to combine short-term risk with long-term equilibrium, rather than relying on the high correlation or cointegration commonly used in pairs trading. The strategy switches dynamically between mean-variance and power-utility objectives, with the latter formulated as stochastic control and solved numerically through a Hamilton–Jacobi–Bellman equation using the Deep Galerkin method.

The machine-learning approach uses clustering to define bands, followed by optimization within those bands. In simulations generated from the same cointelation model, the authors report an advantage for machine learning over the financial mathematics method. That evidence is limited to model-generated data from the assumed framework; the excerpt gives no market-data validation, performance measures, or implementation details. It therefore does not establish whether the relative advantage carries over to live trading or alternative data-generating processes.

Key ideas

• The study compares financial mathematics and machine learning for dynamic portfolios of two intertwined assets.
• The cointelation model is designed to represent both short-term risk and long-term equilibrium.
• The financial mathematics strategy switches between mean-variance and power-utility approaches.
• The power-utility problem is solved numerically using an HJB equation and the Deep Galerkin method.
• A clustering-based machine-learning method outperforms the financial mathematics approach on simulations from the same model.

Tags

# Portfolio Optimization for Cointelated Pairs: SDEs vs. Machine Learning


# Portfolio Optimization for Cointelated Pairs: SDEs vs. Machine Learning









With the recent rise of Machine Learning as a candidate to partially replace classic Financial Mathematics methodologies, we investigate the performances of both in solving the problem of dynamic portfolio optimization in continuous-time, finite-horizon setting for a portfolio of two assets that are intertwined. In Financial Mathematics approach we model the asset prices not via the common approaches used in pairs trading such as a high correlation or cointegration, but with the cointelation model that aims to reconcile both short-term risk and long-term equilibrium. We maximize the overall P&L with Financial Mathematics approach that dynamically switches between a mean-variance optimal strategy and a power utility maximizing strategy. We use a stochastic control formulation of the problem of power utility maximization and solve numerically the resulting HJB equation with the Deep Galerkin method. We turn to Machine Learning for the same P&L maximization problem and use clustering analysis to devise bands, combined with in-band optimization. Although this approach is model agnostic, results obtained with data simulated from the same cointelation model as FM give an edge to ML.

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